Fatigue cracks emanating from sharp notches in high-strength aluminium alloys: The effect of loading direction, kinking, notch geometry and microstructure

The effect of notch geometry on the propagation of fatigue cracks emanating from sharp V-shaped notches was investigated. To this purpose, an experimental campaign has been conducted on Al-7075–T651 specimens carrying notches with aperture angles of 45°, 90°, and 135°. In order to investigate the role of microstructure texture, specimens were extracted from the plates with the main axis either in the longitudinal rolling direction (L-samples) or in the transversal direction (T-samples), or 45° inclined with respect to both directions (LT-samples). The effect of stress amplitude was investigated by performing tests at two load levels. Three loading directions θ = 0°, 45° and 90° were considered. Some specimens experienced pure Mode I loading condition, whereas the remaining ones were subjected to combined Mode I and Mode II loading condition. The crack deflection induced by the variation in loading direction was determined by measuring the kinking angle. A linear elastic fracture mechanics approach was adopted for the analysis of experimental results. Stress intensity factors (SIF) of straight cracks were calculated using an appropriate weight function set up for studying inclined edge cracks emanating from sharp V-notches. On the contrary, a finite element model has been built up to derive the SIFs at the tip of the kinked cracks. The influence of K_II on the crack propagation was discussed on the basis of theoretical and semi-empirical models. It has been found that (i) the crack initiation at the notch root occurred in mixed mode conditions, (ii) a decreasing Mode II component with growing crack length was observed under initial loading direction θ₀ = 45° and θ₀ = 90°, (iii) a crack deflection was observed after 45° rotation of the initial loading direction; a good prediction of the kinking angle was obtained using the maximum tangential stress criterion, and (iv) a fairly good rationalization of all the collected crack growth rate data is obtained if the driving force for crack propagation is expressed in terms of K_I.     

Analysis of mixed-mode cracks in a rubbery particulate composite

The mixed-mode loading of a rubbery particulate composite is studied experimentally. Linear fracture mechanics concepts are used to determine the initiation of growth, the initial growth direction, and the subsequent growth rate for a range of mode mixities. The fracture toughness locus is determined to be elliptical, with the Mode II toughness being lower than its Mode I counterpart. The initial growth directions correlate with maximum strain energy density theories. The crack growth rates can be modeled effectively using an equivalent Mode I crack.     

Mixed-mode fracture in biaxial stress state: Application of the diametral-compression (Brazilian disk) test

Mixed-mode fracture of soda-lime glass was studied using a diametral-compression test that features disk specimens with symmetric through-cracks. The test enables one to study fracture under pure mode I loading, pure mode II loading, or any combination of mode I and mode II loading by a simple alignment of the crack relative to the diameter of compression loading. The disk specimens were precracked with the aid of both chevron notches and water-assisted subcritical crack growth. The directions of noncoplanar crack extensions and the relative magnitudes of mode I and mode II stress-intensity factors for mixed-mode fracture under inert conditions were compared to the predictions of three different mixed-mode fracture theories. None of the theories was completely adequate to explain the experimental observations, but a maximum hoop stress criterion modified to include second order, nonsingular term in the series solution for the crack-tip region stress gave reasonable agreement with the experimental results.     

Plane strain stress intensity factors for branched cracks

A method of calculating stress intensity factors for branched and bent cracks embedded in an infinite body has been developed. The branches are always assumed to be sharp cracks and are modelled by dislocation distributions. The original crack may be either sharp or of elliptical cross-section with finite root radius. Hence, the method which has a precision ±2%, is also applicable to the study of crack branches emanating from elliptical holes and, approximately, also from notches. The following detailed calculations have been made assuming mode I loading: branched sharp crack with branches of equal and different length, bent sharp crack, and one and two crack branches emanating from the crack with a finite root radius. Bending of a sharp crack under mixed mode loading has also been studied. The criteria of maximum tensile stress and maximum energy release rate used in the study of direction of crack propagation are discussed.     

Mixed-mode crack growth in ductile thin-sheet materials under combined in-plane and out-of-plane loading

Ductile thin-sheet structures, such as fuselage skin or automobile panels, are widely used in engineering applications. These structures often-times are subjected to mixed mode (I/II/III) loading, with stable crack growth observed prior to final fracture. To characterize specific specimen deformations during stable tearing, a series of mixed-mode I/III stable tearing experiments with highly ductile thin-sheet aluminum alloy and steel specimens have been measured by using three-dimensional digital image correlation (3D-DIC). Measurements include (a) specimen’s deformed shape and 3D full-field surface displacement fields, (b) load-crack extension response and (c) crack path during stable tearing, (d) angular and radial distributions of strains and (e) the mixed mode crack-opening displacement (COD, measured at 1-mm from crack tip along crack surface) variation as a function of crack extension. Results indicate that for both aluminum alloy and steel at all mixed-mode I/III loading conditions (Φ = 30°, 60° and 90°), the crack tip fields have almost identical angular and radial polar strain distributions. The mixed mode I/III fields were different from those observed for the nominal Mode I loading case (Φ = 0°). The effect of the Mode III loading component is that it lowers the magnitude of the dominant strain component ε _θθ ahead of the growing crack tip and increases the singularity of the strain as compared with that in the mode I case. In addition, measurements indicate that the average mixed mode I/III stable COD for AL6061-T6 (GM6208 steel) is 4×(3×) greater than the average Mode I stable COD.     

Failure criteria for mixed mode delamination in glass fibre epoxy composites

Critical strain energy release rate of glass/epoxy laminates using the virtual crack closure technique for mode I, mode II, mixed-mode I + II and mode III were determined. Mode I, mode II, mode III and mixed-mode I + II fracture toughness were obtained using the double cantilever beam test, the end notch flexure test, the edge crack torsion test and the mixed-mode bending test respectively. Results were analysed through the most widely used criteria to predict delamination propagation under mixed-mode loading: the Power Law and the Benzeggagh and Kenane criteria. Mixed-mode fracture toughness results seem to represent the data with reasonable accuracy.     

Interaction between tensile strength failure and mixed mode crack propagation in concrete

Crack size and structure size transitions are illustrated which connect the two limit-cases of ultimate tensile strength failure (small cracks and small structures) and mixed-mode crack propagation (large cracks and large structures). The problem of mixed-mode crack propagation in concrete is then faced. By increasing the size-scale of the element the influences of heterogeneity and cohesive crack tip forces disappear and crack branching is governed only by the linear elastic stress-singularity in the crack tip region. It is proved in this way that the fracture toughness of the material is measured by a unique parameter (G_IF, G_IC or K_IC) even for the mixed-mode condition. The ratio of the sliding or Mode II fracture toughness (G_IIF, G_IIC or K_IIC) to the opening or Mode I fracture toughness depends only on the crack branching criterion adopted and not on the material features. Eventually, very controversial experimental results recently obtained on the shear fracture of concrete are explained on the basis of the above-mentioned size-scale transition.     

Mechanisms of mixed mode fatigue crack propagation at rail butt-welds

In the present paper, the fatigue crack propagation of longitudinal flaws starting in butt-welded joints of rails is analysed. Firstly Finite Element simulations are carried out, in order to determine the actual stress intensity factor histories caused by the passage of the wheel over the rail. Simulations show that fatigue crack growth is dominated by an out-of-phase Mode I–Mode II mechanism with an overlapping of about 180 degrees. Then, mixed-mode fatigue test experiments have been designed in order to reproduce in-service conditions at laboratory test level. For this purpose, tubular specimens have been subjected to mixed-mode loading (reversal torsion combined with axial tension/compression). The crack growth propagation dominated by the shear has been confirmed. At the end of the paper, the conditions to obtain the shear mode crack propagation are discussed and the kinetics data are presented.     

Numerical analysis of blunting of a crack tip in a ductile material under small-scale yielding and mixed mode loading

The blunting of the tip of a crack in a ductile material is analysed under the conditions of plane strain, small-scale yielding, and mixed mode loading of Modes I and II. The material is assumed to be an elastic-perfectly plastic solid with Poisson's ratio being 1/2. The stress and strain fields for a sharp crack under mixed mode loading are first determined by means of elastic-plastic finite element analysis. It is shown that only one elastic sector exists around the crack tip, in contrast with the possibility of existence of two elastic sectors as discussed by Gao. The results obtained for a sharp crack are used as the boundary conditions for the subsequent numerical analysis of crack tip blunting under mixed mode loading, based on slip line theory. The characteristic shapes of the blunted crack tip are obtained for a wide range of Mode I and Mode II combinations, and found to resemble the tip of Japanese sword. Also the stress field around the blunted crack tip is determined.     

Influence of overloads and block loading sequences on Mode III fatigue crack propagation in A469 rotor steel

A study has been made of the influence of variable amplitude loading on Mode III (anti-plane shear) fatigue crack propagation in circumferentially-notched cylindrical specimens of ASTM A469 rotor steel (yield strength 621 MN/m²), subjected to cyclic torsional loading. Specifically, transient crack growth behavior has been examined following spike and fully-reversed single overloads and for low-high and high-low block loading sequences, and the results compared to equivalent tests for Mode I (tensile opening) fatigue crack growth. It is found that the transient growth rate response following such loading histories is markedly different for the Mode III and Mode I cracks. Whereas Mode I cracks show a pronounced transient retardation following single overloads (in excess of 50% of the baseline stress intensity), Mode III cracks show a corresponding acceleration. Furthermore, following high-low block loading sequences, the transient velocity of Mode I cracks is found to be less than the steady-state velocity corresponding to the lower (current) load level, whereas for Mode III cracks this transient velocity is higher. Such differences are attributed to the fact that during variable amplitude loading histories. Mode III cracks are not subjected to mechanisms such as crack tip blunting/branching and fatigue crack closure, which markedly influence the behavior of Mode I cracks. The effect of arbitrary loading sequences on anti-plane shear crack extension can thus be analyzed simply in terms of the damage accumulated within the reversed plastic zones for each individual load reversal. Based on a micro-mechanical model for cyclic Mode III crack advance, where the crack is considered to propagate via a mechanism of Mode II shear (along the main crack front) of voids initiated at inclusion close to the crack tip, models relying on Coffin-Manson damage accumulation are developed which permit estimation of the cumulative damage, and hence the crack growth rates, for arbitrary loading histories. Such models are found to closely predict the experimental post-overload behavior of Mode III cracks, provided that the damage is confined to the immediate vicinity of the crack tip, a notion which is consistent with fractographic analysis of Mode III fracture surfaces.     

Quantitative fractography of mixed-mode fracture in an R-curve material

Mixed-mode fracture surfaces of an R-curve material were quantitatively assessed using fractography. The R-curve material chosen was a mica glass ceramic. Vickers indentation cracks of different sizes were introduced at the center of tensile surface of glass ceramic bars fractured in flexure. The bars were fractured in flexure by generating mixed-mode (I/II) loading conditions at crack tips by orienting indentation cracks at various angles with respect to the tensile axis. Quantitative fractography indicated that crack-to-mirror size ratios were a function of crack length and mode mixity. Stress intensity at branching for the mirror–hackle transition during mixed-mode (I/II) fracture condition was a constant and was less than the corresponding stress intensity at branching in mode I loading. An empirical relationship is derived for the effective geometric factors in mixed-mode fracture of ceramics from surface cracks in flexure.     

Fatigue crack paths for inclined cracks and surface flaws under biaxial loading

Two approaches are developed for geometrical modeling of crack growth trajectories for the inclined through thickness central cracks and the part-through surface flaw respectively. The principal feature of such modeling is the determination of crack growth direction and the definition of crack length increment in this direction. The damage process zone size concept is employed for calculations of mixed-mode crack growth trajectories and surface flaw shape and positions. Crack front behavior for a straight-fronted edge crack in an elastic bar of circular cross-section is studied through experiments and computations under axial tension loading. The elaborated theoretical model is applied for fatigue crack shape simulation of part-through cracks in a hollow thick- and thin-walled cylinders under different biaxial loading conditions. Suggested approach of crack paths modeling is used for an analysis and prevention of operation failures of existing in-service aircraft gas-turbine engine rotating components.     

SEMI-ELLIPTICAL FATIGUE CRACK GROWTH UNDER ROTATING OR REVERSED BENDING COMBINED WITH STEADY TORSION

Abstract— An analysis of the influence of steady torsion loading on fatigue crack growth rates under rotating or reversed bending is presented. Mixed-mode (I + III) tests were carried out on cylindrical specimens in DIN Ck45k steel and results are compared for two different testing machines: rotary bending and reversed bending obtained by cyclic Mode I (Δ K ₁) with or without superimposed static Mode III ( K _III) loading, simulating the real conditions on power rotor shafts where many failures occur. The growth and shape evolution of semi-elliptical surface cracks, starting from a chordal notch on the cylindrical specimen surface, was measured for several Mode III/ Mode I ratios. Results have shown that the steady Mode III loading superimposed on the cyclic mode I leads to a significant reduction in the crack growth rates. It is suggested that this retardation is related to an increase of plastic zone size near the cylindrical surface in association with the interlocking of rough fracture surfaces, friction and fretting debris, leading to a decrease of the ΔK effective at the crack tip profile due to the "crack closure effect". This work provides a contribution to a better understanding of crack growth rates under mixed-mode load conditions thereby allowing one to predict remaining lifetimes and to estimate the risks of pre-cracked rotor shafts.     

THE INFLUENCE OF NOTCH PLASTICITY ON SHORT FATIGUE CRACK BEHAVIOUR

Abstract— A study has been made of fatigue crack formation and growth at the root of different notch profiles in a structural steel subjected to fully reversed tension-compression loading. The scale of stage I microstructural crack growth at notches decreased with increasing notch root strain and was comparable to the size of stage I cracks in shallow hourglass profile specimens at the same strain. Stage II crack growth rates were faster within the notch plastic field than in the elastic stress field of the bulk material.     

Cracks propagation and interaction in an orthotropic elastic material: Analytical and numerical methods

An elastic orthotropic material containing a crack in Mode I is considered to formulate a new analytical model. The boundary conditions for the crack existence in the material lead to the solution of the homogeneous Riemann–Hilbert problems. The mathematical model was elaborated for a single and two collinear cracks of different lengths and distance for Mode I in order to investigate cracks interaction problem. Using the theory of Cauchy’s integral and the numerical analysis, the fields in the vicinity of the crack tips were determined.Finite Element Method was applied to compare the mathematical analytical solution and to determine the fields in the vicinity of the crack tips. The critical values of applied stress which caused cracks propagation were evaluated. The interaction of cracks in an orthotropic aramid-epoxy material was studied in details. Comparison of both approaches to crack propagation leads to the conclusion that the new analytical model is correct and can be applied to more complex cracks geometries, including inclined cracks.     

Short fatigue crack growth behavior under mixed-mode loading

Mixed-mode loading represents the true loading condition in many practical situations. In addition, most of the fatigue life of many components is often spent in the short crack growth stage. The study of short crack growth behavior under mixed-mode loading has, therefore, much practical significance. This work investigated short crack growth behavior under mixed-mode loading using a common medium carbon steel. The effects of load mixity, crack closure, and load ratio on short crack growth behavior were evaluated by conducting experiments using four-point bending specimens with several initial K _II /K _I mixed-mode ratios and two load ratios. Cracks were observed to grow along the paths with very small K _II /K _I ratios (i.e. mode I). The maximum tangential stress criterion was used to predict the crack growth paths and the predictions were found to be close to the experimental observations. Several parameters including equivalent stress intensity factor range and effective stress intensity factor range were used to correlate short crack growth rates under mixed-mode loading. Threshold values for short cracks were found to be lower than those for long cracks for all the mixed-mode loading conditions. Crack closure was observed for the entire crack length regime with all load mixity conditions at R ≈ 0.05 and for short crack regime under high load mixity condition at R = 0.5. Several models were used to describe mean stress effects and to correlate crack growth rate data.     

Crack propagation in monolithic ceramics under mixed mode loading

Finite element calculations are presented for a semi-infinite crack in a brittle solid undergoing microcracking normal to the maximum tensile direction. Microcracks are presumed stable and a saturation stage is postulated wherein the effective elastic moduli attain steady state values. Mode I, mode II and mixed mode loading conditions are investigated. In these two latter cases, the method of analysis employed allows for cracks to grow out of their initial planes. The mixed mode loading case investigated corresponds to taking equal values of the remote mode I and II stress intensity factors. Contrary to what is observed in the mode I case, no appreciable R-curve behavior is found under mode II or mixed mode conditions.

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Résumé On présente des calculs par éléments finis pour une fissure semi-infinie dans un corps fragile comportant une micro-fissuration normale par rapport à la direction des tensions principales. On suppose que les microfissures sont stables et on postule un stade de saturation au cours duquel les modules d'élasticité atteignent des valeurs constantes. Les conditions de sollicitation en Mode I, et Mode II et en mode mixte sont étudiées et, dans les deux derniers cas, la méthode d'analyse utilisée autorise les fissures à croître hors de leur plant initial.Le mode mixte de mise en charge étudiée revient à prendre des valeurs égales pour les facteurs d'intensité des contraintes agissant à distance selon les Modes I et II.A l'inverse de ce que l'on observe dans le cas du Mode I, on ne trouve pas de comportement significatif selon une courbe R pour les conditions en Mode II et en mode mixte.

     

FATIGUE BEHAVIOUR OF STEEL CASTINGS CONTAINING NEAR-SURFACE DEFECTS

Manufacturing defects in the near-surface region of 2¼% Cr 1% Mo castings were investigated in a joint research programme. After ultrasonic testing and X-ray inspection, large push-pull specimens (cross section 1000 mm²) were taken from castings in regions with indications of defects and tested under fully reversed loading in the elastic and elastic plastic region up to predetermined levels of defect growth. The defects are micropores, pin holes, slag and oxide layers or inclusions, hot tears and small micro cracks in welds. The initiation of crack growth was analysed by two methods, namely (a) the local strain concept with idealization of defects as three-dimensional elliptical notches and (b) by the fracture mechanics concept with idealization of defects as two-dimensional elliptical cracks. The main results can be summarized as follows: 1. The local strain concept describes the crack initiation potential of the defects more accurately than the fracture mechanics concept. 2. Interpretation of casting defects as cracks produces very conservative estimates in many cases. 3. Analytical evaluation of crack growth behaviour using the fracture mechanics approach for defects experiencing crack growth of at least 1 mm is much more accurate than when defects having a smaller extent of crack growth are included in the analysis. Additional evaluations of crack growth behaviour of hot tears by fracture mechanics show that crack growth starting from open and partially closed hot tears must be subjected to a larger number of cycles than normal fatigue cracks of sound material. Partially closed hot tears in the vicinity of the crack front additionally delay crack propagation.     

SHEAR FATIGUE CRACK GROWTH: A LITERATURE SURVEY

A fatigue crack is often initiated by a localized cyclic plastic deformation in a crystal where the active slip plane coincides with the plane of maximum shear stress. Once a crack is initiated, the crack will propagate on the maximum shear plane for a while and, in the majority of the cases, will eventually change to the plane of the applied tensile stress. The “shear” and “tensile” modes of fatigue crack propagation are termed stage I and stage II fatigue crack growth. They are also known as mode II and mode I fatigue crack growth. However, the mechanism of the tensile mode fatigue crack propagation is shear in nature. Considerable progress has been made recently in the understanding of mode II fatigue crack growth. This paper reviews the various test methods and related data analyses. The combined mode I and mode II elastic crack tip stress field is reviewed. The development and the design of the compact shear specimen are described and the results of fatigue crack growth tests using the compact shear specimens are reviewed. The fatigue crack growth tests and the results of inclined cracks in tensile panels, center cracks in plates under biaxial loading, cracked beam specimens with combined bending and shear loading, center cracked panels and the double edge cracked plates under cyclic shear loading are reviewed and analyzed in detail.     

History effect in fatigue crack growth under mixed-mode loading conditions

Plastic deformation within the crack tip region introduces internal stresses that modify subsequent behaviour of the crack and are at the origin of history effects in fatigue crack growth. Consequently, fatigue crack growth models should include plasticity-induced history effects. A model was developed and validated for mode I fatigue crack growth under variable amplitude loading conditions. The purpose of this study was to extend this model to mixed-mode loading conditions. Finite element analyses are commonly employed to model crack tip plasticity and were shown to give very satisfactory results. However, if millions of cycles need to be modelled to predict the fatigue behaviour of an industrial component, the finite element method becomes computationally too expensive. By employing a multiscale approach, the local results of FE computations can be brought to the global scale. This approach consists of partitioning the velocity field at the crack tip into plastic and elastic parts. Each part is partitioned into mode I and mode II components, and finally each component is the product of a reference spatial field and an intensity factor. The intensity factor of the mode I and mode II plastic parts of the velocity fields, denoted by dρ_I/dt and dρ_II/dt, allow measuring mixed-mode plasticity in the crack tip region at the global scale. Evolutions of dρ_I/dt and dρ_II/dt, generated using the FE method for various loading histories, enable the identification of an empirical cyclic elastic–plastic constitutive model for the crack tip region at the global scale. Once identified, this empirical model can be employed, with no need of additional FE computations, resulting in faster computations. With the additional hypothesis that the fatigue crack growth rate and direction can be determined from mixed-mode crack tip plasticity (dρ_I/dt and dρ_II/dt), it becomes possible to predict fatigue crack growth under I/II mixed-mode and variable amplitude loading conditions. To compare the predictions of this model with experiments, an asymmetric four point bend test system was setup. It allows applying any mixed-mode loading case from a pure mode I condition to a pure mode II. Initial experimental results showed an increase of the mode I fatigue crack growth rate after the application of a set of mode II overload cycles.